In this article, we present a simplified model to describe the dynamics of two groups of pedestrians moving in opposite directions in a corridor.The model consists of a $2\times 2$ system of conservation laws of mixed hyperbolic-elliptic type.We study the basic properties of the system to understand why and how bounded oscillations in numerical simulations arise.We show that Lax-Friedrichs scheme ensures the invariance of the domain and we investigate the existence of measure-valued solutionsas limit of a subsequence of approximate solutions.